Available online at ScienceDirect. Energy Procedia 50 (2014 )

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1 Available online at ScienceDirect Energy Procedia 50 (2014 ) The International Conference on Technologies and Materials for Renewable Energy, Environment and Sustainability, TMREES14 Simulation of Hybrid Photovoltaic/Thermal Air Systems on Building Facades Georgios A. Vokas a, Nikolaos G. Theodoropoulos b *, Demos P. Georgiou b a Assist. Prof. of TEI Piraeus, Dep. of Electronics Engineering, P.Ralli & Thivon 250, GR 12244, Greece b University of Patras, Department of Mechanical & Aeronautics, Thermal Engines Lab., Rion Patras, 26500, Greece Abstract The aim of this study is the simulation of a Photovoltaic Thermal (PV/T) Air system on the building façade in order to examine its characteristics and improve its output. Improved efficiency of such systems is achieved by the reduction of the Photovoltaic cell s temperature since the temperature of the cell is reversely proportional to its efficiency. The reduction of temperature can be achieved by placing a heat water or air recovering system, which may transport the heat inside the building for the indoor heating and/or water heating for domestic use. Furthermore, a simulation method of using the Photovoltaic/ Thermal air system on the façade of a building complemented by conventional systems is developed, aiming at covering the needs for warm water usage as well as the indoor central heating and air-conditioning of a building. Finally, a theoretical application of these systems on various houses is studied in order to examine the benefits and the financial constraints of the application Elsevier Ltd. This is an open access article under the CC BY-NC-ND license 2014 The Authors. Published by Elsevier Ltd. ( Selection and peer-review under responsibility of the Euro-Mediterranean Institute for Sustainable Development (EUMISD). Selection and peer-review under responsibility of the Euro-Mediterranean Institute for Sustainable Development (EUMISD) Keywords: Photovoltaic thermal collector; Hybrid systems; Solar heating; NOCT; PV panel efficiency 1. Introduction Nowadays, the percentage of PV systems in electrical energy generation and supply is very low. Such a situation occurs as a consequence of three basic reasons: the low efficiency of the PV systems, the big space that is needed for * Corresponding author. Tel.: ; fax: address: theoniko@mech.upatras.gr Elsevier Ltd. This is an open access article under the CC BY-NC-ND license ( Selection and peer-review under responsibility of the Euro-Mediterranean Institute for Sustainable Development (EUMISD) doi: /j.egypro

2 918 Georgios A. Vokas et al. / Energy Procedia 50 ( 2014 ) the placement of the PV collectors and the individual equipment that constitute the whole system, and finally the high cost [1]. One of the main drawbacks related to the PV technology is that from the absorbed solar radiation by a PV module, only 5 15% is converted into electricity and the rest is emitted to the environment as waste heat which leads to an increase of the cell temperature and reduction of its efficiency [5]. According to each PV module specifications, there is a thermal coefficient that indicates the decrease of power per degree rise in temperature. PV thermal application (PV/T) is separated to two different parts, including the PV module that turns solar radiation into energy and the thermal solar technology which converts solar radiation into heat [7]. There are several PV/T topologies which can be applied in a building for covering a percentage of cooling and heating needs. The PV/T collector can be classified to water PV/T collectors, combination of water/air PV/T collectors and air PV/T collectors. Moreover, the collector might include an absorber collector underneath the flat plate and it can also be glazed or unglazed. Additional glazing improves the heating of the air but decreases the electrical efficiency of the PV module. In any way, the air or water cools the PV module surface and increases slightly its efficiency [19]. A comparison among the efficiency of a PV/T air collector, a solar collector and a PV module has shown that the first mentioned presents always higher overall energy efficiency [9]. In addition to the improvement of the total efficiency of the system, a hybrid PV/T system provides remarkable space reductions compared with the space needed for two separate conventional systems; a PV and a solar system [6]. By integrating the hybrid PV/T collector on a façade, a reduction in the total efficiency of the hybrid PV/T system is expected since the collector does not have the appropriate angle to the solar irradiation. Not many studies that analyze and simulate the operation characteristics of such systems are performed. Although the slightest research has been performed for the hybrid PV/T systems on the façade of a building, some important studies related to the subject have been developed. According to Sarhaddi et al. the thermal efficiency of a PV/T collectors system is inversely proportional to the inlet air temperature, to the wind speed as well as to the increase of the duct length. On the other hand an increase in the inlet air velocity leads to an increase in the thermal efficiency of the PV/T collectors system [9]. Moreover, efforts have been made from Sukamongol et al. for developing a simulation model in order to predict the performance of a condenser heat recovery combined with a PV/T air heating collector, regenerating desiccant trying to reduce the energy used in an air conditioning room under certain meteorological conditions. The comparison between the experimental and the simulated results by the model showed that there is a negligible deviation between them under the same meteorological conditions. Furthermore, the combination of the PV/T air heater with the heat recovered from the condenser, may lead to an energy saving of the air conditioning system up to 18% [11]. Nomenclature c the collector s area, c equal to 1.32m 2 C min the smaller of the two fluid capacitance rates in the heat exchanger C p the specific heat of the air d the distance between the absorber plate with the PV elements and the rear surface F R the heat removal factor of the collector F. R n the characteristic parameter of the collector which shows how the energy is absorbed F. R U L the characteristic parameter of the collector which shows how the energy is lost the collector heat exchanger efficiency factor F' the Fin efficiency factor G T the solar radiation at N.O.C.T. equal to 800 W/m 2 G the gravitational force equal to 9.81[m/s 2 ] h the heat transfer coefficient between the absorber plate and the back surface of the collector h r,p-b the heat transfer coefficient with radiation between absorber plate with the PV cells and the rear surface h w the wind heat transfer coefficient the monthly average daily radiation incident on the collector H

3 Georgios A. Vokas et al. / Energy Procedia 50 ( 2014 ) the solar irradiation () n the transmittance absorbance product and I () the solar irradiation which absorbed by the absorber plate of the collector. I sc the short circuit current k the thermal conductivity K b the back insulation thermal conductivity K e the insulation conductivity L the monthly total heating load for space heating L b the back insulation thickness L e the edge insulation thickness of the collector L/D h the ratio of the lenght of the collector due to the characteristic diameter of the collector p the perimeter of the PV/T collector P mp the peak power n T the thermal efficiency of the collector the number of the glass covers Nu the Nusselt number n mp,(pv/t) the electrical efficiency of the PV/T air collector n mp,(pv) the electrical efficiency of the PV collector n mp,ref.,(pv/t) the maximum power point efficiency of the PV/T air collector at reference conditions n mp,ref the maximum power point efficiency of the PV collector at reference conditions q u the energy flow Q u the useful energy the ambient temperature b the temperature of rear surface of collector f = ( b +T c )/2 T in the inlet air temperature in the collector T ref the collector s temperature at reference conditions. This temperature is received equal to 25 C pm the mean temperature of the absorber plate T pv the PV collector s temperature U L the overall loss coefficient U t the top loss coefficient U e the edge loss coefficient U b the bottom loss coefficient V mp the peak power voltage V oc the open circuit voltage V w the wind speed on the surface of the collector the thermal diffusivity of the air: =, [m 2 /s], the tilt of the collector the volumetric dilation of fluid factor and for ideal gases it is = 1/ f the temperature difference between the two surfaces in [ o K] g the emittance of the glass p the emittance of the plate P,mp,(PV/T) the PV/T air efficiency temperature coefficient P,mp,(PV) the PV efficiency temperature coefficient the kinematic viscosity in [m 2 /s] the Stefan-Boltzmann constant the pollution coefficient, equal to 1 the temperature correction coefficient () () the correction factor because of the place of collector and the season of year

4 920 Georgios A. Vokas et al. / Energy Procedia 50 ( 2014 ) the fluid mass flow rate 2 Research Definition An alternative and probably more effective solution to all the previously mentioned concepts seems to be the hybrid PV/T systems. Many studies, concentrated on estimating some basic economic and performance comparisons between varieties of hybrid PV/T systems, have shown that the cost as well as the performance of two separate systems, a PV and a solar, is higher than the one of a hybrid PV/T system due to common components and space reduction [4, 12, 13, 14, 35]. An important amount of theoretical as well as practical surveys have been conducted during the last years. Many researchers examined the efficiency, the cost as well as the design of different PV/T collectors and PV/T air heater systems [15, 16, 17, 19]. Using different types of thermal collectors as well as new materials for PV cells introduced a variety of implementations such as solar cooling, solar greenhouse, water desalination, solar still, building integrated PV/T (BIPVT) solar collectors and PV/T solar heat pump/air conditioning system [20, 32]. A novel building integrated PV/T system has been designed from Yin et al. for energy efficiency buildings. Silicon PV modules are installed between transparent protective layer and a functionally graded material layer in order to create multifunctional roofing system able to gather solar energy through PV and heat, as well as eliminate the PV efficiency loss and the material redundancies of conventional PV systems [34]. Kim et al. proposed an airtype building integrated photovoltaic-thermal system. In this study the electrical and thermal performance of the BIPVT system was analysed as well as the energy performance of the building having the before mentioned system installed as a building envelope [35]. Kamthania et al. suggested that the electrical efficiency of a semi-transparent PV module is higher compared to the opaque PV module. In their study the performance of a hybrid PV/T double pass façade system using semitransparent PV modules for space heating was presented [36]. A prototype PV/T system was presented by Athienitis et al., [37]. Daghigh et al., in their study underlined the importance and the difficulty of cooling the PV cell in order to improve the efficiency of a PV/T system in hot and humid climate. This is the reason that constitutes water based PV/T collectors systems more attractive and effective than air based systems under this certain conditions [38]. The most recent developments in flat plate PV/T collector systems in terms of their design, performance and applications are presented by Ibrahim et al. [39]. Corbin and Zhai calculated the thermal and electrical performance of a novel building integrated PV/T system using a fluid dynamics model. In this research the effect of active heat recovery on cell performance and the performance of the system as solar hot water heater was examined [40]. The performance of PV/T solar heat pump air-conditioning system was investigated by Fang et al., [41, 10]. 3 Analysis In this study a simulation of a plain PV collector, of a conventional solar air heater and of a hybrid PV/T air collector has been made. Furthermore, a comparison between the plain PV module and the PV/T air collector electrical efficiency as well as a comparison of the thermal efficiency of the solar air heater and the hybrid PV/T air collector has been done. For a precise simulation of the hybrid PV/T air system model all equations and technical data have to be derived first. All the analytical calculations of the basic collector variables are performed by proper utilisation of the corresponding analytical equations of flat solar air collectors, [21]. However, it should be noted that PV cells are considered as the absorber as far as these equations are concerned. On the following Fig. 1 a hybrid PV/T air collector is represented in an intersection. According to the planning the airflow goes through in between the absorbing plate and the insulation.

5 Georgios A. Vokas et al. / Energy Procedia 50 ( 2014 ) Fig. 1. Intersection of a typical PV/T air collector. The PV module used is SQ 160-C model of the Shell company [22]. The total surface of the SQ 160-C model is 1.32 [m 2 ]. The electrical characteristics for the cells temperature equal to 25 o C and under Standard Test Conditions, (S.T.C.) as well as the typical characteristics of the collector under nominal operational conditions temperature of the PV cells (N.O.C.T.) are presented on the Tables 1 and 2. The analysis which used for the estimation of the efficiency is presented in Appendix 3. The results are then compared in order to derive the differences of the two systems and are represented on the Table 8. Moreover, the electrical efficiency of the PV/T air collector as well as that of the PV collector for different collector s temperature was calculated and the results are presented in the Fig. 6. Table 1. Electrical characteristics of SQ 160-C collector into S.T.C. [23] Parameters Peak Power, P mp Peak Power current, I mp Peak Power voltage, V mp Open circuit voltage, V oc Short circuit current, I sc Values 160 W 4.58 A 35 Volt 43.5 Volt 4.9 A 3.1 Mean monthly energy output Table 2. Electrical characteristics of the SQ 160-C collector into N.O.C.T. [23] T PV P mp V mp V oc I sc Parameters at N.O.C.T. Values 46 o C 115 W 32 Volt 40 Volt 3.95 A The mean monthly energy output E in [kwh] of a PV collector as well as of a PV/T air collector is determined by the following equation [23]: and E H A C el. (1) a 1 30 T (2) The results of the temperature correction coefficient for the region of Patras as well as the mean monthly ambient temperature are presented on the Table 3. According to the above analysis the result of the mean monthly energy

6 922 Georgios A. Vokas et al. / Energy Procedia 50 ( 2014 ) output of the PV/T air collector as well as of the PV collector on the façade of the building in the region of Patras, are represented in the following Fig Monthly Energy output PV collector PV/T air collector E [kw] Month Fig. 2. Results of the mean monthly energy output of the PV /T air collector as well as of the PV collector per m Thermal characteristics for the f-chart method The calculation of the thermal efficiency of the PV/T air collector as well as a solar collector was estimated by using the f-chart method. This method calculates the percentage of the total thermal load that can be covered with the solar energy for a specific heating system, [24]. This research examines a PV/T air system which main objective is to cover the annual demand for hot air that provides heat together with other conventional systems, such as the natural gas boiler. F-chart method uses the mean monthly thermal load, while it requires the average monthly incidence solar radiation H on the surface of the PV/T air collector, [33]. The available average monthly data of the solar radiation for the region of Patras was calculated according to the equations that are presented in [2]. Patras latitude is 35.5, while the collectors tilt is 90, [2]. All the results are represented on the Table 4. Furthermore, the calculated monthly mean solar radiation for the region of Patras is presented in the following Fig. 3. GJ Monthly Mean Solar Radiation Month Fig. 3. The results of the monthly incidence solar radiation (H ) on the surface of the PV/T air collector. The f-chart method also requires the average monthly domestic load, [33]. In order to calculate the monthly mean thermal loads of the building, the mean temperature of the ambient of Patras is derived by Bazeos s study [25]. The domestic heating consumption (L H ), is calculated by using the Degree-Days method of Kreider and Rabl, [26]. The mean temperature of the absorber plate is always larger than the mean liquid temperature as a result of the heat transfer resistance between the absorber plate and the liquid. This temperature difference is usually small for the solar liquid collectors, but still important for the air collector systems. In the present study the temperature of the collector from the equation that represents the mean temperature of the absorber plate T c,m was assigned assuming that T c = T c,m, [1].

7 Georgios A. Vokas et al. / Energy Procedia 50 ( 2014 ) Q u A T C c Tp,m T 1F f,in F U R R L (3) where Q u is the useful energy and is calculated from the equation:.... Q u AcF R I U n L T in T (4) To define the coefficient () different experimental studies have been done and numerous analytical equations have been given. A typical coefficient value of () is 0.74 for PV/T collectors and 0.85 for conventional solar collectors, [27, 29]. In order to calculate all the analytical equations as well as the thermal coefficient of the PV/T air collector and of the conventional solar air collector, [30], the data on the Table 6 had been considered. The thermal efficiency of the PV/T air collector is calculated from the equation, [24]. Ti T nt FR F n RUL (5) G T According to several experimental calculations arises that the temperature of the PV panels varies between 5 o C to 60 C, while 50 C is considered to be a mean temperature, [3, 31]. Therefore, for these calculations a 50 C temperature was used as the temperature of their PV collector. According to the above analysis, the thermal efficiency of the PV/T air collector and of the thermal air collector was calculated. The results are presented in the Fig Results and discussion 4.1 Results of the thermal characteristics for the f-chart method According to the above analysis and using the equations (8) to (26), the thermal efficiency of the hybrid PV/T air collector and of the thermal air collector were calculated. The results are presented in the following Fig. 4a. T 0,5 0,45 0,4 0,35 0,3 0,25 0,2 0,15 0,1 0,05 0 Estimation of the Thermal efficiency Thermal air collector PV/T air collector Itterations Tc PV/T air collector Thermal air Collector Iterations (a) (b) Fig. 4a,b. (a) The results of the thermal efficiency of the PV/T collector and of thermal air collector during the repetitive calculations. (b) The results of the temperature of the collector, Tc, during the repetitive calculations. The values of the several factors of the hybrid PV/T air collector and of the conventional solar air collector are calculated and presented in Table 7. The preceding calculations were repeated eight times until the results of the mean plate temperature and the thermal efficiency converge. Furthermore, in Fig. 4b the results of the temperature of

8 924 Georgios A. Vokas et al. / Energy Procedia 50 ( 2014 ) the hybrid PV/T air collector as well as the temperature of the thermal collector during the iterations are shown. 4.2 Results of the electrical efficiency All the results from the analysis for investigating the electrical efficiency are presented in Table 8. Moreover, the electrical efficiency of the hybrid PV/T air collector as well as that of the PV collector for different collector s temperatures was calculated and the results are presented in the graph of Fig. 5. el 0,14 0,12 0,1 0,08 0,06 0,04 0,02 0 PV/T air collector PV collector Temperature [ o C] Fig. 5. The results of the electrical efficiency of the hybrid PV/T air collector and of the PV collector for different collector s temperature. 4.3 Results of the f-chart method The results of the monthly thermal domestic load covered by the hybrid PV/T air system as well as by the solar air system are presented in the graph of Fig. 6. f[%] The percentage of monthly thermal domestic loads PV/T air system Solar air system Month 5 Conclusions Fig. 6. Monthly thermal domestic load covered by the hybrid PV/T air system as well as by the Solar air system. As it was shown the PV/T air collector improved the efficiency of the PV collector by extracting the produced heat and using it to cover the thermal loads of the building. In specific, all the characteristics of the PV/T air collector in order to specify the electrical efficiency have been calculated. Furthermore, the estimation of the thermal efficiency of the hybrid collector was calculated and found to be equal to 37.15%, while the outlet air temperature from the collector was found to be o C. What derives from the previous analysis, the thermal efficiency of the PV/T air collector as well as the efficiency of the conventional solar air collector is very low. This happened because of the inclination that the collectors are integrated, (both the PV/T air collector and the conventional solar air collector are integrated on the façade of a

9 Georgios A. Vokas et al. / Energy Procedia 50 ( 2014 ) building). A further analysis of both efficiencies shows that when the PV/T air collector is used, an efficiency reduction around 5.59% takes place. This reduction is low and permits the usage of the hybrid systems. After the estimation of the thermal efficiency, the electrical efficiency was also calculated. In order to verify the growth of the electrical efficiency, the electrical efficiency of the conventional photovoltaic collector was also calculated and presented in the above table. As a result the total efficiency of the two systems (the conventional solar collector and the photovoltaic collector) was found to be equal to 46.32% and 52.38% corresponding. A first look at these two efficiencies leads to the fact that the PV/T air collector is less efficient than the conventional system. However, the area that these two systems need should be considered. The PV/T air collector produced this efficiency in a surface of (2x1.32)m 2 = 2.64m 2. Thus this comparison leads to the conclusion that the PV/T air collector is sufficient and its use on the façade of the building could be a convenient choice. Furthermore, the coverage of the domestic thermal loads has been calculated. The appropriate method that was used was the f chart method. According to the calculations that were presented in the Table 8 for the region of Patras and for a total surface area of 30m 2 was 6.5%. Therefore, the amount that was resulted from the domestic thermal loads was covered by the PV/T air system. As it was resulted, the percentage coverage of the thermal loads is not big because of the fact that the PV/T air collector was integrated on the façade of the building. This inclination affects the façade of the hybrid collector since the collector does not face the sun in the appropriate angle. Appendix A. Table 3. The thermal characteristics used for the calculations of the hybrid PV/T air collector. Parameters Values Kg/sec C P 1006 J/kg.o C A C 1.32 m 2 c 0.5 C min 1006 J/kg.o C Table 4. The hybrid PV/T air collector s input data as well as the conventional solar air collector s input data [30]. Parameters Values PV/T Air Collector Conventional Solar Air Collector T a 293 o K 293 o K T in 293 o K 293 o K p g h w 9.5 W/m 2.o C 9.5 W/m 2.o C 5.67E-08 W/m 2.o C 5.67E-08 W/m 2.o C A c m m Kg/sec Kg/sec C 1007 J/(kg.o C) 1007 J/(kg.o C) G T 800 W/m W/m 2 I T 2.88 MJ/m MJ/m 2 K b W/m.o C W/m.o C L b 0.05 m 0.05 m K e W/m.o C W/m.o C L e m m p L 0.04 m 0.04 m N 1 1 T pm 298 o K 298 o K b h ca 45 W/m 2.o C 45 W/m 2.o C K abs 390 W/m.o C 390 W/m.o C L abs m m K pv 84 W/m.o C 84 W/m.o C L pv 0.04 m 0.04 m n

10 926 Georgios A. Vokas et al. / Energy Procedia 50 ( 2014 ) Table 5. The results of the monthly temperature correction coefficient for the region of Patras. Month T a Values o C o C o C o C o C o C o C o C o C o C o C o C Table 6. Monthly domestic heating load at the region of Patras. Month m h DD h Total loads, L Values yr Total Average 17,586 Table 7. Calculated values of the hybrid PV/T air collector. Appendix B. Electrical efficiency Parameters Values PV/T Air Collector Conventional Solar Air Collector U b 0.9 W/m.o C 0.9 W/m.o C (UA) e W/m.o C W/m.o C U e W/m.o C W/m.o C U t W/m.o C W/m.o C U L W/m.o C W/m.o C h r,p-b W/m.o C W/m.o C L/D h 80.6 Nu k W/m.o C W/m.o C h W/m.o C 3.88 W/m.o C F' F R Q u MJ 1.62 MJ q u 1.07 MJ/m MJ/m 2 F. R U L W/m.o C W/m.o C F. R n pm The equation for calculating the electrical efficiency of the PV/T air collector is, [24]: mp,(pv/t) mp,ref(pv/t) P,mp,(PV/T) c ref n n (6)

11 Georgios A. Vokas et al. / Energy Procedia 50 ( 2014 ) The equation for calculating the electrical efficiency of the PV collector is [24]: mp mp,ref.,(pv) P,mp.,(PV) c ref n n (7) The efficiency at the higher possible point of the PV collector under the reference conditions was calculated and under N.O.C.T. conditions and cell s temperature equal to 45 C from the equation, [24]: n mp,ref I A mp C V mp G T (8) The temperature that is developed on the PV/ air collector for N.O.C.T. conditions is calculated and found equal to 66.4 o C. According to the information sheet of the PV collector the power of the collector is increased 0.52% for every degree for collector s temperature decrease, [29]. As a result the increase in collector s temperature of 20.4 o C, results to a decrease of the PV/T air collector s power equal to 10.59Watts. Therefore, the PV/T air collector s power is 104.4Watts. The efficiency at the higher possible point of the PV/T air collector under N.O.C.T. conditions is calculated from the following equation, [24]: n mp,ref.,(pv/t) P A mp,(pv/t) C G T (9) P,mp ) coefficient is calculated from equation (10), while the temperature P,mp.(PV/T) ) coefficient is calculated from equation (11): Voc P,mp n mp,ref (10) Vmp Voc P,mp.,(PV/T) n mp,ref.,(pv/t) (11) Vmp.,(PV/T) Voc is the temperature coefficient for the open circuit voltage and is represented by the equation: oc V,oc dv Voc T2 Voc T1 dt T T 2 1 (12) Voc coefficient two values of the open circuit voltage for different temperatures are necessary. According to the characteristics of the PV cell as represented in the Fig. 7, for ref = 25 C or 298 K and for a radiation level 1000W/m 2, V oc = 43.25Volts arises. Furthermore, for T = 50 o C the V oc = 39.5Volts. Table 8. Results of the electrical characteristics. Parameters Values n mp,ref(pv) n mp,ref(pv-t) 0, Voc P,mp(pv) P,mp(pv-t) -0, n mp,(pv) 0,09842 n mp,(pv-t) 0,09642

12 928 Georgios A. Vokas et al. / Energy Procedia 50 ( 2014 ) Appendix C. The temperature of the collector The temperature that is developed in a hybrid PV/T air collector is not equal to the temperature developed in a common PV cell. The temperature of the collector is calculated by the equation [1]: 1 F T T n G FU R c i T T (13) R L Consequently, a new parameter, the heat removal factor (F R ) that is calculated by the equation (14) should be appointed, since it describes the ability of the working fluid to remove heat from the fin and collector [1, 24, 29]: ACULF' C p Cp FR 1e AC UL (14) where U L is calculated from the equation: U L Ut Ub Ue (15) where U b and U e are calculated by the equations: and U K b b (16) Lb C e UA Ue (17) A e UA e K p L (18) L e where U t is the heat losses coefficient of the front surface of the collector as represented in the following equation, [24, 27]: U t where: T pm 2 2 pm 1 N 1 2N f c p w g e Tpm T 1 N f hw p N (19). h w V w (20) c (21)

13 Georgios A. Vokas et al. / Energy Procedia 50 ( 2014 ) w w p f h h (22) 100 e T pm (23) The fin efficiency factor of the collector, F, is represented by the following equation, [1, 24]: 1 F' UL 1 1 h 1 1 h h r,p b (24) The equation that represents the coefficient h is: k Nu h (25) D h where D h is the characteristic diameter of the collector. In this case, the characteristic diameter is calculated from the equation: D h 2 d (26) Hollands et.al. [28], suggest that the Nusselt number for heat transfer by conduction between the air in the parallel plates in tilt (between 0, 60 ), with Rayleigh number between 0 and 105 and with a balanced temperature, should be given by the equation that follows: 1/6 * 1/3 * sin1.8 Ra cos Nu Ra cos (27) where, the asterisk, (*), indicates that only positive values have to be taken. If the value within the bracket is negative, take it as zero. The equation is also used for an up to 90 tilt with satisfactory results. This is the reason why in this research this equation was used. The Reyleigh number was calculated by the following equation: 3 g Ra v (28) References [1] Kaplanis SN. Solar engineering. Athens: Ion Press; [2] Kagarakis K. Photovoltaic Technology. Athens: Symmetria Press; [3] Sorensen B. PV power and heat production: an added value. In: H. Scheer et al. James and James, eds. Proceedings of the 16th European Photovoltaic Solar Energy Conference, Glasgow. p [4] Tiwari A, Sodha MS. Performance evaluation of hybrid PV/thermal water/air heating system: A parametric study. Renewable Energy 2006; 31: [5] Tonui J, Tripanagnostopoulos Y. Improved PV/T solar collectors with heat extraction by forced or natural air circulation, Renewable energy 2006; 32: [6] Vokas GA, Christantonis N, Skitides F. Hybrid photovoltaic thermal systems for domestic heating and cooling A theoretical approach.

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